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Solve x2 + 8x -12 = 0 by completing the square x2 + 8x =12 x2 + 8x + 16 = (x + 4)2 =28 x + 4 = +Ö 28 x=-4 +2Ö7 } { -4 +2Ö7 }

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**6.3: Relationship of Roots, Factoring, Graphing & Solving Equations**

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If A*B = 0 then A= 0 or B = 0

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**(x+2) (x-3) = 0 (x+2)=0 or (x-3) = 0 x= -2 or x=3 x2 – x - 6= 0**

Solve by factoring: x2 – x - 6= 0 (x+2) (x-3) = 0 (x+2)=0 or (x-3) = 0 x= -2 or x=3 {-2, 3}

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**Equation: Factors: (x+2) (x-3) Solutions: Roots: { -2,3} Graph:**

-2 and 3 x-int at -2 and 3

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**Equation: Factors: (x-p)(x-q) Solutions: Roots: {p, q} Graph: p and q**

MULT. and make it = 0 Equation: Factors: Solutions: Roots: Graph: (x-p)(x-q) {p, q} p and q x-int at p and q

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**2x2 +7x = 15 2x2 +7x – 15 = 0 (2x-3) (x+5) = 0 (2x-3)=0 or (x+5)= 0**

Solve by Factoring: 2x2 +7x – 15 = 0 (2x-3) (x+5) = 0 (2x-3)=0 or (x+5)= 0 2x=3 or x=-5 x=3/2 or x=-5

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**5x2 – 60=5x 5x2 - 5x – 60 = 0 5(x2 - x – 12) = 0 5(x-4) (x+3)= 0**

Solve by Factoring: 5x2 - 5x – 60 = 0 5(x2 - x – 12) = 0 5(x-4) (x+3)= 0 5=0 x-4=0 or x+3= 0 x=4 or x=-3

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**Equation: x2 + 5x = 0 Factors: x(x+5) Solutions: Roots: {0, –5 }**

Graph: x(x+5) {0, –5 } 0 and -5 x-int at 0 and -5

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**Write two equations that has roots of ½ and –3/4**

(x – ½) (x + 3/4 ) =0 x2 + 3x/4 – x/2 – 3/8 = 0 x2 + 1x/4 – 3/8 = 0 8x2 + 2x – 3 = 0

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**Find two consecutive odd**

integers whose product is 195 x (x+2) = 195 x2 + 2x = 195 x2 + 2x – 195 = 0 (x-13)(x+15) =0 x-13 = 0 or x+15 =0 x=13 x=-15 13 & 15 or -15 &-13

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**2x2 +7x - 15 2x2 +7x – 15 =y Roots: 3/2 and -5 (2x – 3) (x + 5)**

Factor by graphing: 2x2 +7x – 15 =y Roots: 3/2 and -5 Factors: (x – 3/2) (x+5) (2x – 3) (x + 5) Check: 2x2 +7x - 15

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**4x2 - 100 4x2 - 100 =y Roots: 5 and -5 4(x – 5) (x + 5) Factor by**

graphing: 4x =y Roots: 5 and -5 Factors: (x – 5) (x+5) Check: x2 – NO! 4(x – 5) (x + 5)

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Complex Numbers Objectives:

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